Methoid and apparatus for generating a 3d model of an object

ABSTRACT

A method for generating a 3D model for fabricating a multi-material object using additive manufacturing. The method comprises providing a first volumetric model of an object in a deformed configuration, generating a second volumetric model from the first volumetric model and assigning materials to the second volumetric model by: a) defining a cluster of elementary volumetric elements of the second volumetric model, b) selecting a cluster object material in the database of object materials by minimizing a cost function determined by computing a deformed configuration of the second volumetric model under a set of predefined loads and constraints, c) partitioning the elementary volumetric elements of the cluster in two sub-clusters based on the deformed configuration, d) repeating step b) for each sub-clusters. The method further comprises generating a 3D model for fabricating an object from the second volumetric model and the assigned materials.

FIELD OF THE INVENTION

The instant invention relates the design and fabrication ofmulti-material objects from 3D models.

More precisely, the invention relates to methods and apparatus forgenerating 3D models of multi-material objects.

BACKGROUND OF THE INVENTION

Additive manufacturing (AM) is understood as any process in which athree-dimensional object is synthetized from a 3D model.

The field of additive manufacturing has gathered tremendous interest inrecent year, allowing for the production of personalized on-demandobjects with shapes or geometries that may even be impossible tomanufacture using traditional technics.

Various AM techniques exist such as stereolithography, fused depositionmodeling, 3D inkjet printing, also known as Polyjet™ (Stratasys Ltd.,North America), Continuous Liquid Interface Production (CLIP) or thelike.

A three-dimensional object may typically be formed by sequential-layermaterial addition/joining throughout a 3D work envelope under automatedcontrol. However, several novel AM techniques do not involve suchsequential-layer addition. On example is Continuous Liquid InterfaceProduction.

While traditional techniques such as stereolithography or fuseddeposition modeling involve a single consumable material, recentadvances in the field have led to the possibility of producingmulti-material object made from several materials with differingphysical properties (color, density, elasticity, etc.).

One example of such novel manufacturing methods is 3D inkjet printing inwhich building materials are selectively jetted from one or moreprinting heads and deposited onto a fabrication tray in consecutivelayers according to a pre-determined configuration defined by a softwarefile. The printing head may be, for example, an ink jet head providedwith a plurality of dispensing nozzles arranged in an array of one ormore rows along a longitudinal axis of the printing head.

These multi-material manufacturing technics have opened the way forfabricating realistic complex objects with varying physical propertiessuch as color, density, elasticity, etc.

Multi-colored objects are straightforward applications of thesetechniques but many other applications shows great potential.

Among these new applications, the possibility of controlling thedeformation properties of an object is of particular interest forcopying real-life objects in a convincing manner or designing novelcomplex objects.

One example of application is related to surgical training and medicaldevice development and testing in which benchtop devices realisticallyreproducing the behavior of an organ could be of great interest fortraining surgeon to perform surgery or testing medical device in reallife conditions.

Among other fields, the invention can thus find applications in surgicaltraining and medical device development and testing.

However, while a multi-colored object is relatively easy to design,generating a 3D model for fabricating an object with controlled elasticproperties has proved to be more difficult.

Indeed, while the color of an object is a local physical property, thedeformation of the object results from global interactions between thevarious parts of the object. The selection and positioning of materialswithin the object thus involve a global computation of the dynamicbehavior of the object.

Additional difficulties come from the limitation on the number ofmaterials for fabricating the object. While newer 3D printers are ableto print ever-increasing numbers of materials, the range of materialsavailable at a given time on a given apparatus is in practice alwayslimited.

Moreover, printing materials are primarily selected on the basis oftheir printing properties and the range of physical properties is thusalso limited.

The algorithms currently used to design multi-material 3D model ofobjects with controlled physical properties are thus often trouble toconverge to an accurate or printable solution, or requires exponentialcomputing power.

One approach for reducing the computing power and increasing theconvergence speed and stability of the algorithm is to assume that theelementary parts constituting the object are mechanically dependent onlyalong one dimension of space, and are mechanically independent from eachother in the two other directions of space. This way, the combinationspace of the 1D sequence of materials is limited and can be exploredwith classical combinational techniques.

Such an approach is described for instance in U.S. Pat. No. 8,565,909.It can be used for the generation of 3D models of layered objects suchas a footware sole.

However this approach cannot be extended to the design of object withthree-dimensionally varying mechanical properties and multi dimensionsmechanical interactions with environment (stress load, boundaryconditions . . . ) without an exponential increase in computing powerand time and a strong decrease in convergence stability.

Another approach is described for instance in “Interactive MaterialDesign Using Model Reduction” by Hongyi Xu, published in ACMTransactions on Graphics, Vol. 34, No. 2, Article 18, Publication date:February 2015. This approach aims at solving the combinationaloptimization problem by first determining a continuous material alongthe object with varying properties. The continuous distribution ofmaterial is then discretized in individual elementary material volumesbased on the printing materials offered by a given printer.

However, this approach does not guarantee that the final object, madewith a limited number of materials, will show accurate elasticproperties.

In particular, in many cases, the physical properties of the materialsare not regularly spaced from one another along the full range ofphysical properties. A discrete optimization process then often producesmore accurate results.

Eventually, some approaches have been specifically designed fortwo-material objects and are based on a linear interpolation betweensaid two materials followed by a step of driving the linear combinationobtained toward each of the two materials.

“Computational Design of Actuated Deformable Characters” by MelinaSkouras et al. Published in ACM Transactions on Graphics (TOG)—SIGGRAPH2013 Conference Proceedings TOG Homepage Volume 32 Issue 4, July 2013details such a method.

Such two-material approach cannot be extended to the design of objectwith a plurality of N>2 materials without degrading the convergence ofthe algorithm.

There is thus a need for a method for generating a 3D model forfabricating a multi-material object which would offer an accuratesolution for a large range of manufacturing materials, an improvedconvergence speed and reliability and require less computing power thanthe prior art.

SUMMARY OF THE INVENTION

To this aim, a first object of the invention is a method for generatinga 3D model for fabricating a multimaterial object using additivemanufacturing, the method comprising:

providing a first volumetric model of an object in at least a deformedconfiguration,

generating a second volumetric model from said first volumetric model,said second volumetric model being divided in a plurality of elementaryvolumetric elements,

assigning to each elementary volumetric element of the second volumetricmodel a material selected in a database of M object materials byperforming at least the following steps:

a) defining a cluster of elementary volumetric elements of the secondvolumetric model,

b) selecting a cluster object material in the database of objectmaterials by minimizing a cost function of said cluster determined bycomputing at least one deformed configuration of the second volumetricmodel under set of predefined loads and constraints at least oneelementary volumetric element of said cluster has been assignedintrinsic material properties associated to a material of the databaseof object materials,

c) partitioning the elementary volumetric elements of said cluster in atleast two subclusters based on the deformed configuration of saidcluster,

d) repeating at least once step b) for each of said at least twosubclusters, and

generating a 3D model for fabricating an object from the secondvolumetric model and the materials assigned to each elementaryvolumetric element of the second volumetric model.

In some embodiments, one might also use one or more of the followingfeatures:

-   -   said cost function is a function of a deformed configuration of        the cluster and the deformed configuration of the first        volumetric model;    -   step b) comprises an operation b1) of computing a deformed        configuration cost function of the second volumetric model,        associated to at least one material of the database of object        materials, said operation b1) comprising:

b1-1) assigning to each elementary volumetric element of said clusteridentical intrinsic material properties associated to said material,

b1-2) determining a deformed configuration of the second volumetricmodel under the set of predefined loads and constraints,

b1-3) computing a cost function of said cluster associated to saidmaterial, said cost function being a function of a strain error betweenthe deformed configuration of said cluster and the deformedconfiguration of the first volumetric model;

-   -   said operation b1) of computing a deformed configuration cost        function of the second volumetric model is performed for each        material of a subset of M materials of the database of object        materials,

and step b) further comprises an operation b2) of selecting a clusterobject material in the database of object materials by comparing thecost functions computed for each material in said subset of materials ofthe database of object materials;

-   -   an ordered subset of M materials of the database of object        materials is associated to a cluster of the second volumetric        model,

and the materials of said ordered subset are ordered according to aphysical property of said materials, in particular according to astiffness of said materials;

-   -   said operation b1) of computing a deformed configuration cost        function of the second volumetric model is performed for a        preselected material in the ordered subset of M materials of the        database of object materials, and step b) further comprises the        operations of:

b2) comparing a function of said cost function to a terminationcriterion to determine whether said preselected material can be selectedas the cluster object material,

b3-1) if said preselected material can be selected as the cluster objectmaterial perform step c),

b3-2) if said preselected material cannot be selected as the clusterobject material, preselecting another material in said subset of Mmaterials of the database of object materials by comparing said costfunction to a direction criterion and reiterate at least once operationsb1) through b3-1), b3-2);

-   -   each elementary volumetric element of the cluster of the second        volumetric model is respectively associated with at least one        elementary volumetric element of the first volumetric model;    -   step c) comprises an operation c1) of comparing a location of at        least one elementary volumetric element in the deformed        configuration of the cluster with a location of at least one        elementary volumetric element in the deformed configuration of        the first volumetric model;    -   the step of partitioning the elementary volumetric elements of        the cluster in at least two subclusters comprises an operation        c2) of determining, for each subcluster of said at least two        subclusters, a subset of materials of the database of object        materials associated to said subcluster on the basis of the        deformed configuration of the cluster;    -   steps b) and c) are repeated until each subclusters comprise a        single elementary volumetric element;    -   steps b) and c) are repeated until a difference between the        deformed configuration of the second volumetric model and the        deformed configuration of the first volumetric model of the        object satisfy a convergence criterion;    -   the first volumetric model is provided by:

receiving a three dimensional model of an object comprising at least onesurface mesh representative of an interface of the object, in particularan interface of the object associated to a discontinuity in the physicalproperties of the object,

generating the first volumetric model from said three dimensionalsurface mesh by performing a volumetric model generation, for instancefinite element volumetric model generation;

-   -   the set of predefined loads and constraints comprise a load on        said interface of the object;    -   the database of object materials comprises a plurality of 3D        printed materials and, optionally, additional metamaterials        and/or nonprintable materials such as water, gels, metals, ions,        ceramics, biomolecules and the like.

Another object of the invention is an apparatus for generating a 3Dmodel for fabricating a multi-material object using additivemanufacturing, the apparatus comprises at least:

a memory unit operative to store at least a first volumetric model of anobject, set of predefined loads and constraints to be applied on thefirst volumetric model of the object and a deformed configuration of thefirst volumetric model of the object under the set of predefined loadsand constraints,

a processing unit operative to

generate a second volumetric model from said first volumetric model,said second volumetric model being divided in a plurality of elementaryvolumetric elements,

assign to each elementary volumetric element of the second volumetricmodel a material selected in a database of M object materials by:

a) defining a cluster of elementary volumetric elements of the secondvolumetric model,

b) selecting a cluster object material in the database of objectmaterials by minimizing a cost function of said cluster determined bycomputing at least one deformed configuration of the second volumetricmodel under the set of predefined loads and constraints at least oneelementary volumetric element of said cluster has been assignedintrinsic material properties associated to a material of the databaseof object materials,

c) partitioning the elementary volumetric elements of said cluster in atleast two subclusters based on the deformed configuration of saidcluster,

d) repeating at least once step b) for each of said at least twosubclusters, and

generate a 3D model for fabricating an object from the second volumetricmodel and the materials assigned to each elementary volumetric elementof the second volumetric model.

BRIEF DESCRIPTION OF THE DRAWINGS

Other characteristics and advantages of the invention will readilyappear from the following description of several of its embodiments,provided as non-limitative examples, and of the accompanying drawings.

On the drawings:

FIG. 1 is a flow chart illustrating the operations of a method forgenerating a 3D model according to an embodiment of the invention,

FIG. 2 is a flow chart detailing the sub-steps of the operation ofassigning a material to each elementary volumetric element of the secondvolumetric in the method of FIG. 1,

FIG. 3 illustrates an embodiment of a first volumetric model of theinvention in an initial configuration,

FIG. 4A to 4C illustrates successive steps of partitioning the secondvolumetric model in clusters during the operation of assigning amaterial to each elementary volumetric element of the second volumetricof FIG. 2,

FIG. 5 illustrates examples of first and second volumetric model whereinthe object is a copy of an original object which is a portion of a humanorgan, and

FIG. 6 illustrates an embodiment of an apparatus for generating a 3Dmodel for fabricating a multi-material object according to theinvention.

On the different figures, the same reference signs designate like orsimilar elements.

DETAILED DESCRIPTION

FIGS. 1 and 2 illustrate a method for generating a 3D model forfabricating a multi-material object using additive manufacturingaccording to a first embodiment of the invention.

The fabricated multi-material object presents controlled deformations,meaning that, under predefined loads and constraints (Stress field,Volumetric forces, Boundary conditions), the object takes a targetdeformation configuration.

In one non-limitative example of realization illustrated on FIG. 5, theobject is a copy of an original object which is a portion of a humanorgan.

This approach for fabricating objects with desired deformation behaviorhas a number of distinct steps that are summarized on FIG. 1 anddetailed hereafter.

First, the mechanical properties of the object materials that theprinter/fabricator has to work with are measured and characterized. Thiscan be done ahead of time and stored as intrinsic material propertiesassociated to each material of a database of object materials stored inelectronically-readable storage.

By “mechanical properties” and “mechanical behaviors”, it is meant forinstance uni-axial or multi-axial tensile strength or modulus, uni-axialor multi-axial compressive strength or modulus, shear strength ormodulus, coefficient of static or dynamic friction, surface tension,elasticity.

The database of object materials may comprise a plurality of 3D printedmaterials.

The object materials may exhibit linear mechanical behaviors but alsonon-linear, hyper-elastic stress-strain mechanical behaviors.

The physical behavior of the materials can be represented by definingintrinsic material properties.

The intrinsic material properties comprise functions modeling thephysical behavior of a material. For instance the intrinsic materialproperties can include a density of a material, Young Modulus, Poissonratio, thermal conductivity, electric conductivity. The intrinsicmaterial properties may also take into account non-linear effects in thematerial.

The intrinsic material properties define for instance a stress-strainrelationship as a function of the local strain ε(u). The stress-strainrelationship can be stored as a matrix E and parameterized by a set ofparameters. The parameters can be static values or function of variousparameters, for instance a non-linear function of strain. The matrix Ecan thus also represents a non-linear function E(p(u)).

In some embodiments, additional metamaterials and/or non-printablematerial may be included in the database of object materials.

Metamaterials are microstructures of materials whose mechanicalproperties may be averaged over the structures to be assimilated to anequivalent homogeneous material.

Non-printable materials comprise for instance non-polymerizablematerials. Such non-printable materials may for instance comprise water,gels, metals, ions, ceramics, bio-molecules and the like.

These object materials may also be provided by a 3D printer but usuallydon't have to be polymerized during the printing process and may stayfluid or liquid in the object. The size of the sub-region of the objectmade solely from these non-printable materials may thus be limited insome specific application of the invention in order to ensure themechanical stability of the object.

A first step of the method is illustrated on FIG. 1 and comprisesproviding a first volumetric model VM1 of an object. The firstvolumetric model is for instance received by an input unit of anapparatus for generating a 3D model as detailed further below.

In some embodiment, the first volumetric model may also be generated bythe apparatus for generating a 3D model.

The first volumetric model comprises a three-dimensional set of nodeswhich defines a plurality of elementary volumetric elements partitioninga first space region modeled by the first volumetric model.

The three-dimensional set of nodes and the elementary volumetricelements of the first volumetric model are defined in order to be ableto perform a three-dimensional numeric simulation of the deformations ofthe first volumetric model. Examples of such numeric simulation arefinite element simulation, discrete element method, combined finiteelement-discrete element method and the like.

The elementary volumetric elements are for instance selected among theshapes of tetrahedron, pyramid, triangular prism and hexahedron. Inparticular, tetrahedrons may be selected as elementary volumetricelements.

The first volumetric model may in particular comprise unstructured grid,i.e. tessellation of the first space regions in an irregular pattern.

This way, the first volumetric model may be adapted to present a refinedstructure where spatial variations of deformations of the mesh arelocally high.

The first volumetric model may in particular be generated from a threedimensional surface mesh by performing a volumetric model generation,for instance finite-element volumetric model generation for example byusing a software such as “Abaqus” ® by Dassault System Inc.

The first volumetric model may for instance be generated and received byan apparatus for generating a 3D model as follow.

A three dimensional model of an object comprising at least one surfacemesh representative of an interface of the object may be received.

By “surface mesh” it is meant a three-dimensional surface which may beclosed or open. The three-dimensional surface may be a CAD model or apolygon mesh and may be tessellated or defined by a set of equations.

The interface of the object may for instance be associated to adiscontinuity in the physical properties of the object.

In one embodiment, the three dimensional model of the object isgenerated on a computer, for instance by using a 3D modeling software.

In another embodiment, the three dimensional model of the object may beacquired from measurements of a physical original object copied by themanufacturing object.

The measurements may comprise a 3D scanning of the object and/orvolumetric measurements, in particular non-invasive measurements, forinstance if the object is an internal part of a larger object thatshould not be destroyed, for instance living tissues.

By “a non-destructive measurement of an imaged region located inside theheterogeneous object” it is mean a measurement of a local physicalparameter of a region located inside the heterogeneous object withoutdamaging said object. Nondestructive imaging methods are known in thefield of medical imaging and comprise for instance Radiography, MagneticResonance Imaging (MRI), Ultrasound, Elastography, Tactile imaging,Photoacoustic imaging, Thermography, Echocardiography, Functionalnear-infrared spectroscopy, Tomography, Computer-assisted Tomographysuch as X-ray computed tomography, Positron emission tomography orMagnetic resonance imaging and Nuclear medicine such as Scintigraphy orSingle-photon emission computed tomography for instance.

A volumetric measurement typically output a three dimension scalar fieldor vector field of an imaged region. In the case of a three-dimensionalscalar field, the volumetric measurement usually comprises a set ofthree-dimensional pixels, commonly referred as “voxel” (short for“volumetric pixel”) juxtaposed with one another along the threedimensions. A scalar or vector field representative of the localphysical parameter in a voxel may be associated to every voxel. Thescalar field is for example a locally measured density (enlarged to thevoxel).

A surface mesh of the object may then be determined by performing atopological segmentation of the measurement.

Such a topological segmentation can be automatically performed byapplying an image processing algorithm, adapted to identify clusters ofthree-dimensional pixels in the three dimensional model of an imagedregion according to:

-   -   the local physical parameter associated to each voxel (minimal        density, density with regard to the neighboring voxels), and    -   constrains on the geometric properties of the voxel clusters        (for example a minimal size or a specific shape of an organ).

Then, a surface reconstruction process—for example a “marching cubes”method—may be implemented to build a three-dimensional surface mesh ofthe object from the output of the topological segmentation operation.

The surface mesh is thus a three-dimensional surface which delimits aboundary of a cluster of voxel identified during the topologicalsegmentation operation.

In one particular example of the invention, the surface mesh may be aninternal interface of a larger object, delimiting the original object.The original object may then for instance be an organ or a portion of anorgan inside a body and the surface mesh may be an interface of saidorgan.

Several surface meshes may be determined for each organ or organ portionidentified in the imaged region.

Surface meshes may be part of the three dimensional model of the imagedregion.

This embodiment may be combined with the previous embodiment, i.e. thethree dimensional model of the physical original object may be modifiedon a computer, for example by using a 3D modeling software, in order tomake an object that is not an attempt at a copy but has differentcharacteristics than the original object.

The first volumetric model VM1 is then generated from said threedimensional surface mesh by performing a volumetric model generation,for instance finite-element volumetric model generation.

The first volumetric model is provided in at least a deformedconfiguration VM1-CD illustrated on FIG. 4A.

By a “configuration of a volumetric model”, it is meantthree-dimensional locations of the nodes which defines the plurality ofelementary volumetric elements partitioning the space region modeled bythe volumetric model.

In an embodiment of the invention, at least two configurations of thefirst volumetric model may be provided.

For instance, an initial configuration of the first volumetric modelVM1-CI (illustrated on FIG. 3) and a deformed configuration of the firstvolumetric model VM1-CD (illustrated on FIG. 4A to 4C)) may be provided.

The deformed configuration of the first volumetric model may also becalled a “target deformed configuration” as explained in greater detailsfurther below.

The initial configuration and the deformed configuration comprisedistinct locations of at least one node, in particular of several or allnodes of the first volumetric model.

The initial configuration and the deformed configuration may bedetermined for several three dimensional surface meshes as detailedabove, for instance by performing several volumetric measurements of aphysical original object copied by the manufacturing object undervarious load conditions. These measurements are similar to themeasurements used to determine the three dimensional model of the objectmentioned before and will not be described again.

The deformed configuration of the first volumetric model may also begenerated on a computer, for instance by using a 3D modeling software orby using a numerical simulation software to compute a deformedconfiguration of the first volumetric model.

In yet another embodiment of the invention, the initial configuration ofthe first volumetric may be generated on a computer or determined byvolumetric measurements of a physical original object copied by themanufacturing object and the deformed configuration may be then bedetermined from the initial configuration by a numerical simulation of adeformation of the initial configuration of the first volumetric under afirst set of predefined loads and constraints. The deformedconfiguration of the first volumetric model of the object may then beassociated to the first set of predefined loads and constraints.

By “a set of predefined loads and constraints”, it is meant the effectof the surrounding environment on the model. The predefined loads andconstraints may thus comprise loads which may be mechanical such asvolumetric forces (gravity), surface forces (loads, pressure), ponctualforces (moment, . . . ), thermic such as thermal load, or electric ormagnetic such as concentrated charge. The predefined loads andconstraints may also comprise boundary conditions which may also bemechanical such as encastrement, displacement/rotation, velocity,general contact, self-contact but also thermal or fluidic such astemperature, acoustic pressure and electric potential. The predefinedloads and constraints may also comprise global environmental effectssuch as temperature field and pressure field (scalar or vector field).

A second volumetric model VM2 is then generated from the firstvolumetric model.

The second volumetric model also comprises a three-dimensional set ofnodes which define a plurality of elementary volumetric elementsdividing a second space region modeled by the second volumetric model.

The properties of the first volumetric model that were described abovecan thus also be applied to the second volumetric model.

The second volumetric model VM2 may be generated from the initialconfiguration VM1-CI of the first volumetric model.

The configuration of the second volumetric model may be similar to theinitial configuration of the first volumetric model, meaning that thelocation of its nodes may be similar. Alternatively, the externalsurface or interface of the second volumetric model only may be similarto the external surface or interface of the second volumetric model andthe internal arrangement of the nodes of the first and second volumetricmodels may be distinct.

The second volumetric model is a model of the fabricated object whosedeformed configuration under a second set of predefined loads andconstraints is intended to be as close as possible to the deformedconfiguration of the first volumetric model.

The second volumetric model may thus mesh a similar space region thanthe first volumetric model and may in general be roughly identical tothe first volumetric model.

Each elementary volumetric element i of the second volumetric model isrespectively associated with at least one elementary volumetric elementi of the first volumetric model.

It should be noted, however, that the second volumetric model may alsoslightly depart from the first volumetric model and/or be adapted totake into account various constrains related to the fabrication process.

Such adaptation can involve a simplification of the topology to ensure areliable or possible manufacturing. Among the manufacturing constraintsare: setting a minimum wall thickness, preventing undercut molding,taking into account the minimal droplet size of the three-dimensionalprinting process (about 16 microns diameter). Additional constraints arerelated to cleaning the support material after the 3D printing. One ormore constraints from the following list can thus be taken into account:

-   -   a minimum size of the elementary volumetric element, for example        each element must contain a cube of dimension 16 μm*16 μm*16 μm,        corresponding to a minimum size of polymerized drops;    -   a geometric parameter relating to the minimum distance g between        two points of the polyhedron, for example by ensuring that        g>a*g, where        g=min_((A,B)belonging to element)|(xA,yA,zA)−xB,yB,zB)| and a is        a predefined scalar.

A second set of Predefined loads and constrains is provided and intendedto be applied on the second volumetric model of the object.

In some embodiments of the invention, the second set of predefined loadsand constraints may be identical to the first set of predefined loadsand constraints used to determine the deformed configuration of thefirst volumetric model. In other embodiments, the second set ofpredefined loads and constraints may depart from the first set ofpredefined loads and constraints, for instance by incorporatingadditional physical phenomenon such as gravity and/or ignoring somephenomenon.

In one non-limitative example of application, the predefined loads andconstraints are representatives of surgical mechanical forces that areexerted on the tissues of the internal element during a predefinedsurgical operation. For example, the second set of predefined loads andconstraints may then comprise an external stress field σ defined tocorrespond to the stress field exerted by a neuroradiologist introducinga catheter in a carotid artery, and deploying a stent in the artery. Theset of predefined loads and constraints may include additional forcefield such as surrounding organs stress field and/or blood pressure.

In such a case, the set of predefined loads and constraints will besimilar to the stress field applied on the inner surface of the carotidartery and for example directed along the outer local normal at eachpoint of the inner surface of the carotid artery with a magnitudesimilar to the magnitude of a force exerted by a stent, typicallybetween 10 and 100 kPa. Once the configurations VM1-CI, VM1-CD of thefirst volumetric model, the second volumetric model VM2 and the set ofpredefined loads and constraints have been provided or generated, themethod according to the invention involves an operation of assigning toeach elementary volumetric element of the second volumetric model amaterial selected in a database of M object materials as illustrated onFIGS. 2 and 4A-4C.

This operation comprises the following general steps that areillustrated on FIGS. 4A to 4C:

a) defining a cluster of elementary volumetric elements of the secondvolumetric model,

b) selecting a cluster object material in the database of objectmaterials by minimizing a cost function of said cluster determined bycomputing at least one deformed configuration of the second volumetricmodel under the second set of predefined loads and constraints whereinat least one elementary volumetric element of said cluster has beenassigned intrinsic material properties associated to a material of thedatabase of object materials,

c) partitioning the elementary volumetric elements of said cluster in atleast two sub-clusters based on the deformed configuration of saidcluster,

d) repeating at least once step b) for each of said at least twosub-clusters.

These general steps will now be described in more details.

During step a), a cluster of elementary volumetric elements of thesecond volumetric model is defined.

When step a) is performed for the first time during the method, thecluster of elementary volumetric elements may comprise the totality ofthe elementary volumetric elements of the second volumetric model.

As the method proceeds, the cluster may comprise a smaller and smallernumber of elementary volumetric elements until it reaches a singleelementary volumetric element as it will become apparent from thefollowing description of the method.

An object material is then selected in the database of object materialsfor the cluster. The selection of the object material for the cluster isobtained as the results of minimizing a cost function of the cluster.

This cost function is a function of the deformed configuration of thefirst volumetric model and a deformed configuration of the clusterdetailed further below and illustrated on FIG. 4A.

The cost function is for instance a function of a strain error betweenthe deformed configuration of the cluster and the deformed configurationof the first volumetric model.

The strain error may in particular be written as ε_(i) ^(M)−ε_(i) ^(T)where ε_(i) ^(M) is a strain of an elementary volumetric element i ofthe cluster between an initial configuration of the second volumetricmodel without the set of predefined loads and constraints and a deformedconfiguration of the cluster under the set of predefined loads andconstraints and ε_(i) ^(T) is a displacement of an elementary volumetricelement i of the first volumetric model between the initialconfiguration of the first volumetric model and the deformedconfiguration of the first volumetric model.

Alternatively, the cost functions may be function of strain, stress,reaction force and the like . . . .

Several cost functions may be used depending on the progress of themethod and/or the size of the cluster.

A first example of a suitable cost function Jg can be written as:

$\begin{matrix}{{Jg} = \sqrt{\frac{1}{n}{\sum\limits_{i = 1}^{n}\left( {ɛ_{t}^{M} - ɛ_{t}^{T}} \right)^{2}}}} & (1)\end{matrix}$

where n is the number of elementary volumetric elements in the clusterand ε_(i) ^(M)−ε_(i) ^(T) is the strain error between the deformedconfiguration of the cluster and the deformed configuration of the firstvolumetric model. This cost function (1) is always positive.

Another example of cost function J_(Cl) is:

$\begin{matrix}{J_{Cl} = {\frac{1}{n}{\sum\limits_{i = 1}^{n}\left( {ɛ_{i}^{M} - ɛ_{i}^{T}} \right)}}} & (2)\end{matrix}$

where n is the number of elementary volumetric elements in the clusterand ε_(i) ^(M)−ε_(i) ^(T) is the strain error between the deformedconfiguration of the cluster and the deformed configuration of the firstvolumetric model. This cost function (2) can be positive or negative.

Yet another example of a suitable cost function J_(i), specificallyadapted for a cluster containing only a single elementary volumetricelement is:

$\begin{matrix}{J_{i} = \frac{ɛ_{i}^{M} - ɛ_{i}^{T}}{ɛ_{i}^{T}}} & (3)\end{matrix}$

where ε_(i) ^(M)−ε_(i) ^(T) is the strain error between the deformedconfiguration of the cluster and the deformed configuration of the firstvolumetric model. This cost function (3) can be positive or negative.

A selected cost function (1)-(3) is computed during an operation b1)which is illustrated in greater detail on FIG. 2 and comprises a firstsub-operation of b1-1) assigning to each elementary volumetric elementof said cluster identical intrinsic material properties associated to aselected material.

The object material may be then selected in a predefined subset of Mmaterials of the database of object materials.

Method for defining said subset of M materials and for selecting theobject material in said subset of M materials are detailed furtherbelow.

Then, during a sub-operation b1-2) a deformed configuration VM2-CD ofthe second volumetric model under the set of predefined loads andconstraints is determined as illustrated on FIG. 4A.

The deformed configuration of the second volumetric model may bedetermined by performing a finite element simulation of the deformationof the second volumetric model under the set of predefined loads andconstraints.

Once the deformed configuration of the second volumetric model has beendetermined, the cost function of the cluster associated to said materialcan be computed b1-3). The cost function is for instance computed fromthe selected equation (1)-(3) detailed above.

In a first embodiment of the invention, operation b1) is performed foreach material of a subset of M materials of the database of objectmaterials.

Each material of the subset of M materials of the database of objectmaterials is thus successively selected, assigned to every elementaryvolume element of the cluster, the deformed configuration of the secondvolumetric model is determined and the associated cost function iscomputed.

Once a cost function has been associated to each material of the subsetof M materials, a cluster object material can be selected (operation b2)in the database of object materials by comparing the cost functions andselecting the object material associated to the lowest cost function forinstance.

In another embodiment of the invention, the subset of M materials of thedatabase of object materials can be ordered according to a physicalproperty of said materials.

The physical property may for instance be selected among the intrinsicmaterial properties, for instance a density of a material, YoungModulus, Poisson ratio, thermal conductivity, electric conductivity.

For instance, the materials in the subset can be ordered based on theirstiffness, from the softest to the hardest, for instance according to amulti-axial tensile modulus.

In this embodiment, step b) may be performed as follows:

A first material may be pre-selected in the ordered subset of Mmaterials of the database of object materials, for instance a materialassociated to a median or mean physical property of the materials of theordered subset.

Then, a first deformed configuration cost function may be computed b1)for said pre-selected material.

Then, a function of the computed cost function, for instance an absolutedifference between the computed cost function and a previously computedcost function, is compared to a termination criterion in an operationb2). The termination criterion is for instance a maximal differencethreshold.

If said function of the computed cost function satisfies the terminationcriterion the pre-selected material can be selected as the clusterobject material in an operation b3-1).

The function of the computed cost function satisfies the terminationcriterion, another material is pre-selected in the subset of Mmaterials.

To this aim, the cost function is compared to a direction criterion, forinstance a direction threshold and another material of the orderedsubset is selected on the basis of the result of said comparison.

An example is illustrated on FIGS. 4B and 4C.

In this example the cost function is computed according to equation (2)which can get positive and negative values. The direction criterion is acomparison with the threshold value 0.

If the cost function is negative, the deformation of the cluster was toosmall with regard to the target deformation, the material is thusupdated to the next softer material of the subset of M materials.

If the cost function is positive, the deformation of the cluster was toohigh with regard to the target deformation, the material is thus updatedto the next stiffer material of the subset of M materials.

Operations b1) through b3) can then be reiterated until the terminationcriterion is met.

The terminal criterion is important to ensure that the algorithm canterminate and don't stay locked oscillating between two materials.

Indeed, since the materials shows a discrete range of physicalproperties, the difference between the deformed configuration of thesecond volumetric model and the deformed configuration can usually notbe reduced to zero.

A remaining error thus has to be accepted and is encoded in thetermination criterion.

The termination criterion may also take into account cases when anextremity of the range of physical property of the subset of material isreached.

When the cluster object material has been selected, the method can moveon to step c).

During step c), the elementary volumetric elements of the cluster arepartitioned in at least two sub-clusters based on the deformedconfiguration of the cluster.

To this aim a location of each elementary volumetric element in thedeformed configuration of the cluster may be compared with a location ofthe associated elementary volumetric element in the deformedconfiguration of the first volumetric model (operation c1).

A number of sub-clusters can be defined to classify the results of thesecomparisons as illustrated on FIGS. 4B and 4C.

As a matter of non-limitative example, three sub-clusters CL1, CL2, CL3are defined in the example of FIG. 4B as follows:

-   -   sub-cluster CL3 comprises the elementary volumetric elements        which are displaced too much in the deformed configuration of        the second volumetric model with regard to the deformed        configuration,    -   sub-cluster CL1 comprises the elementary volumetric elements        which are not displaced enough in the deformed configuration of        the second volumetric model with regard to the deformed        configuration, and    -   sub-cluster CL2 comprises the elementary volumetric elements        which can be considered as being within an acceptable distance        of the deformed configuration.

Of course, more or less sub-clusters may be defined in order topartition more finely or more roughly the cluster.

In addition, or in variant, the partitioning operation may take intoaccount other properties relating to the deformed configuration of thecluster.

An example of higher order property is for instance the normal directionof each elementary volume element with regard to the normal direction ofthe associated element in the deformed configuration.

During this step, a subset of materials of the database of objectmaterials may be associated (operation c2) to each sub-cluster on thebasis of the deformed configuration of the cluster.

As a matter of example, let's define the database of materials ascontaining m materials referenced as Mat_1, . . . , Mat_m and orderedaccording to a measure of the stiffness of said materials as detailedabove.

In this example, we assume that material Mat_k with 1≤k≤m was selectedduring step b). Sub-cluster A, which comprises the elementary volumetricelements that are displaced too much in the deformed configuration ofthe second volumetric model, can then be associated with a subset ofharder materials of the material database, for instance the subsetMat_k, . . . , Mat_m. Sub-cluster B, which comprises the elementaryvolumetric elements that are not displaced enough in the deformedconfiguration of the second volumetric model, can be associated with asubset of softer materials of the material database, for instance thesubset Mat_1, . . . , Mat_k. Sub-cluster C comprises the elementaryvolumetric elements that are considered to have an acceptable behaviorand whose selected material can thus stay identical. The subsetassociated to sub-cluster C can thus be restricted to Mat_k.

Other ways to associate a subset of material to a given sub-cluster canbe defined, for instance by selecting overlapping ranges of materials.

It is understood that, during the first occurrence of step b) in themethod, the cluster may comprise the entire second volumetric model. Thesubset of materials associated to this cluster may then comprise thewhole range of material of the database.

Once the elementary volumetric elements of the cluster have beenpartitioned, steps b) and c) of the method can be repeated for eachsub-cluster of the partition.

The method can then involve a recursive computation on smaller andsmaller cluster until each sub-clusters comprise a single elementaryvolumetric element.

On example is illustrated on FIG. 4C on which sub-cluster CL1 is againdivided in three sub-clusters CL1-1, CL1-2, CL1-3.

Alternatively or in addition, steps b) and c) of the method can berepeated until a difference between the deformed configuration of thesecond volumetric model and the deformed configuration of the firstvolumetric model of the object satisfy a convergence criterion.

For instance, a general cost function of the deformed configuration ofthe entire second volumetric model (for example based on equation 1) maybe computed and compared to a convergence criterion, for instance athreshold on the maximum error over the whole second volumetric model.

If the convergence criterion is met, the reiteration of steps b) and c)can be stopped.

Then, a 3D surface model for fabricating the object may be generatedfrom the second volumetric model and the materials assigned to eachelementary volumetric element of the second volumetric model.

The 3D model may for example comprise a plurality of 3D files such asSTL files (file format native to the stereolithography CAD softwarecreated by 3D Systems, Rock Hill, S.C.). Each file may be associated toa single material of the plurality of material printable by a 3Dprinter. More precisely, each file may correspond to a surface meshdelimiting all the elementary volumetric elements which are associatedwith the same material of the plurality of material printable by a 3Dprinter.

The 3D surface model may be used for manufacturing the object.

The method according to the invention may include the final step offabricating the object.

The fabrication of the object may be performed at least in part byadditive manufacturing in particular by 3D printing.

It is understood by those of ordinary skill in the art that the finalobject can be manufactured using both traditional and state-of-the-artmethods including, but not limited to, casting, 3D printing, mechanicallinkages of disparate materials and material deposition manufacturing.

Additional non-polymerizable materials such as water, gels, metals,ions, ceramics, bio-molecules and the like may be used and may bedeposited using various techniques encompassing casting, 3D printing,mechanical linkages of desparate materials and shape depositionmanufacturing.

In some embodiments, the elementary volumetric elements may bereplicated with a plurality of printed layers, e.g. 5-20 printinglayers.

According to some embodiment of the present invention, a multi-materialadditive manufacturing device able to fabricate the object may beequipped with several building materials, in particular at least twobuilding materials, each having different mechanical properties asdetailed above.

Optionally, the multi-material additive manufacturing device may beequipped to dispense the additional material, e.g. non-printablematerials such as water, gels, metals, ions, ceramics, bio-molecules andthe like.

In one embodiment of the present invention, advanced 3D printingtechnology may be used that enable seamless integration of variousmaterials in the object. For instance, Stratasys, Ltd. (North America,7665 Commerce Way Eden Prairie, Minn. 55344. Phone: +1 952-937-3000 Fax:+1 952-937-0070) produces advanced 3D printers using PolyJet Matrix™Technology that enables a plurality of material durometers to besimultaneously jetted in the production of the same mechanical device,allowing for spatially varying viscoelastic properties within thesimulation device.

With a 16-micron, high-resolution print layer, high dots-per-inch inboth X and Y resolution, and an easy-to-remove support materialproperty, this technology allows to develop simulation device withmechanical properties that are adjusted at the scale of the livingtissues.

The multi-material object fabricated by implementing the method of theinvention may be a physical simulation device. A physical simulationdevice is able to simulate the mechanical behavior of a complex objectsuch as an heterogeneous object or an homogeneous object with complexmechanical behavior that are difficult to reproduce in a manufacturedobject without relying on a combination of several materials.

Among other fields, the physical simulation can find applications insurgical training and medical device development and testing.

As non-limited and non-exhaustive examples, a physical simulation devicecan be an aid for planning surgery, in particular to train surgeons toperform operations using physical simulation devices of living tissues.

Eventually, another object of the invention is an apparatus 500 forgenerating a 3D model for fabricating a multi-material object accordingto a method as detail above.

Such an apparatus is illustrated on FIG. 6 and comprises:

-   -   an input unit 503 operative to receive at least a first        volumetric model of an object, a set of predefined loads and        constraints to be applied on the second volumetric model of the        object and a deformed configurations of the first volumetric        model of the object    -   a memory unit 505 operative to store said first volumetric model        of an object, predefined load to be applied on the second        volumetric model of the object and deformed configurations of        the first volumetric model of the object,    -   a processing unit 504 operative to

generate a second volumetric model from said first volumetric model,said second volumetric model being divided in a plurality of elementaryvolumetric elements,

assign to each elementary volumetric element of the second volumetricmodel a material selected in a database of M object materials by:

a) defining a cluster of elementary volumetric elements of the secondvolumetric model,

b) selecting a cluster object material in the database of objectmaterials by minimizing a cost function of said cluster determined bycomputing at least one deformed configuration of the second volumetricmodel under the set of predefined loads and constraints wherein at leastone elementary volumetric element of said cluster has been assignedintrinsic material properties associated to a material of the databaseof object materials,

c) partitioning the elementary volumetric elements of said cluster in atleast two sub-clusters based on the deformed configuration of saidcluster,

d) repeating at least once step b) for each of said at least twosub-clusters, and

-   -   generate a 3D model for fabricating an object from the second        volumetric model and the materials assigned to each elementary        volumetric element of the second volumetric model, and    -   an output unit 506 able to output said generated 3D model.

To ease the interaction with the computer, a screen 501 and a keyboard502 may be provided and connected to the processing unit 504.

Although many embodiments have been described in reference to generatinga 3D model for fabricating a multi-material object using additivemanufacturing, the embodiments of the present invention are not limitedin that respect and that the same system and methods can be used forfabricating simulating devices of other internal elements.

The terms “comprises”, “comprising”, “includes”, “including”, “having”and their conjugates mean “including but not limited to”. The term“consisting of” means “including and limited to”. The term “consistingessentially of” means that the composition, method or structure mayinclude additional ingredients, steps and/or parts, but only if theadditional ingredients, steps and/or parts do not materially alter thebasic and novel characteristics of the claimed composition, method orstructure.

It is appreciated that certain features of the invention, which are, forclarity, described in the context of separate embodiments, may also beprovided in combination in a single embodiment. Conversely, variousfeatures of the invention, which are, for brevity, described in thecontext of a single embodiment, may also be provided separately or inany suitable sub-combination or as suitable in any other describedembodiment of the invention. Certain features described in the contextof various embodiments are not to be considered essential features ofthose embodiments, unless the embodiment is inoperative without thoseelements.

1.-15. (canceled)
 16. A method for generating a three-dimensional modelfor fabricating a multi-material anatomical model using additivemanufacturing, the method comprising: providing a volumetric model of ananatomic object in a first configuration and in a second configuration,the volumetric model including a plurality of three-dimensional nodeswhich define a plurality of elementary volumetric elements partitioninga first space region modeled by the volumetric model; determiningmechanical properties of the three-dimensional model based on the firstconfiguration and the second configuration, wherein the secondconfiguration is a deform configuration under predefined loads andconstraints; assigning to each elementary volumetric element of thevolumetric model a material selected in a database of plurality ofmaterials by performing at least the following steps: defining a clusterof elementary volumetric elements of the volumetric model, havingidentical mechanical properties; assigning to each elementary volumetricelement of the cluster identical intrinsic material propertiesassociated to the material, wherein the intrinsic material propertiesdefine stress-strain relationship; computing a cost function of thecluster associated to the material, the cost function being a functionof the deformed configuration of the cluster and the deformedconfiguration of the volumetric model; selecting a cluster objectmaterial in the database of plurality of materials by minimizing a costfunction of the cluster; and generating a three-dimensional model forfabricating the anatomic object from the volumetric model and thematerials assigned to each elementary volumetric element of thevolumetric model.
 17. The method according to claim 16, wherein theselecting a cluster object material in the database of plurality ofmaterials by minimizing a cost function of the cluster is performed foreach material in the database of plurality of materials.
 18. The methodaccording to claim 16, wherein the selecting a cluster object materialin the database of plurality of materials by minimizing a cost functionof the cluster further includes comparing the cost functions computedfor each material in the database of plurality of materials.
 19. Themethod according to claim 16, wherein the cost function is a function ofstrain error between the cluster and the volumetric model.
 20. Themethod according to claim 16, wherein the cost function is a function ofstress error between the cluster and the volumetric model.
 21. Themethod according to claim 16, wherein each of the plurality ofelementary volumetric element of the volumetric model in firstconfiguration is respectively associated with each volumetric element ofthe volumetric model in second configuration.
 22. The method accordingto claim 16, wherein the mechanical properties of the three-dimensionalmodel is determined by comparing a location of at least one elementaryvolumetric element in the first configuration with a location of the atleast one elementary volumetric element in the second configuration. 23.The method according to claim 16, wherein the volumetric model isprovided by; receiving a three-dimensional model of an object comprisingat least one surface mesh representative of an interface of the object,in particular an interface of the object associated to discontinuity inphysical properties of the object; and generating the volumetric modelfrom the at least one surface mesh by performing a volumetric modelgeneration.
 24. The method according to claim 16, wherein the predefinedloads and constraints comprise a load on the anatomical model.
 25. Themethod according to claim 16, wherein the predefined loads andconstraints are selected from a list of volumetric forces, surfaceforces, punctual forces, thermal loads, electric charge, and magneticcharge.
 26. The method according to claim 16, wherein the mechanicalproperties of the three-dimensional model is uni-axial.
 27. The methodaccording to claim 16, wherein the mechanical properties of thethree-dimensional model is multi-axial.
 28. The method according toclaim 16, wherein the mechanical properties are selected from a list ofcompressive strength, shear strength, coefficient friction, staticfriction, dynamic friction, surface tension, and elasticity.
 29. Themethod according to claim 16, further includes providing a thirdconfiguration of the volumetric model, wherein the third configurationis a deform configuration under a second predefined loads andconstraints, which is different than the predefined loads andconstraints of the second configuration.
 30. A system for generating athree-dimensional model for fabricating a multi-material anatomic objectusing additive manufacturing, the system comprising; a memory unitoperative to store a volumetric model of an anatomic object in a firstconfiguration and in a second configuration, wherein the secondconfiguration is a deform configuration under predefined loads andconstraints, the volumetric model being divided in a plurality ofelementary volumetric elements, a processing unit operative to assign toeach elementary volumetric element of the volumetric model a materialselected in a database of plurality of materials by: defining a clusterof elementary volumetric elements of the volumetric model havingidentical mechanical properties; assigning to each elementary volumetricelement of the cluster identical intrinsic material propertiesassociated to the material, wherein the intrinsic material propertiesdefine stress-strain relationship; computing a cost function of thecluster associated to the material, the cost function being a functionof the deformed configuration of the cluster and the deformedconfiguration of the volumetric model; selecting a cluster objectmaterial in the database of plurality of materials by minimizing a costfunction of the cluster; and generating a three-dimensional model forfabricating the anatomic object from the volumetric model and thematerials assigned to each elementary volumetric element of thevolumetric model.
 31. The system of claim 30 wherein the mechanicalproperties are selected from a list of compressive strength, shearstrength, coefficient friction, static friction, dynamic friction,surface tension, and elasticity.
 32. The system of claim 30 wherein thepredefined loads and constraints comprise a load on the anatomicalmodel.
 33. The system of claim 30 wherein the selecting a cluster objectmaterial in the database of plurality of materials by minimizing a costfunction of the cluster is performed for each material in the databaseof plurality of materials.
 34. The system of claim 30 wherein themechanical properties of the three-dimensional model is multi-axial. 35.An anatomic object fabricated by three-dimensional model generated bymethod of claim 16, comprising; an organ copy being formed fromplurality of materials; an external surface of the organ copy, whereinthe external surface of the organ copy is associated to discontinuity inphysical properties of the organ copy; and the materials selected from adatabase of plurality of materials are arranged so that the mechanicalproperties of the anatomic object under predefined loads and constraintsmatches the mechanical properties of a scanned physical original objectunder the predefined loads and constraints.